Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Selective and Efficient Quantum Process Tomography without Ancilla

Christian Tomás Schmiegelow, Ariel Bendersky, M. A. Larotonda, Juan Pablo Paz

Published Sep 1, 2011• 46 citations
Publisher

Abstract

Several methods, known as quantum process tomography, are available to characterize the evolution of quantum systems, a task of crucial importance. However, their complexity dramatically increases with the size of the system. Here we present a new method for quantum process tomography. We describe a new algorithm that can be used to selectively estimate any parameter characterizing a quantum process. Unlike any of its predecessors this new quantum tomographer combines two virtues: it requires investing a number of physical resources scaling polynomially with the number of qubits and at the same time it does not require any ancillary resources. We present the results of the first implementation of this quantum device, characterizing quantum processes affecting two qubits encoded in heralded single photons. Even for this small system our method displays clear advantages over the other existing ones.

DOI
10.1103/physrevlett.107.100502

Related papers

Ancilla-less selective and efficient quantum process tomography

Christian Tomás Schmiegelow, Ariel Bendersky, M. A. Larotonda +1 more

Several methods, known as Quantum Process Tomography, are available to characterize the evolution of quantum systems, a task of crucial importance. However, their complexity dramatically increases with the size of the system. Here we present the theory describing a new type of method for quantum process tomography. We describe an algorithm that can be used to selectively estimate any parameter characterizing a quantum process. Unlike any of its predecessors this new quantum tomographer combines two main virtues: it requires investing a number of physical resources scaling polynomially with the number of qubits and at the same time it does not require any ancillary resources. We present the results of the first photonic implementation of this quantum device, characterizing quantum processes affecting two qubits encoded in heralded single photons. Even for this small system our method displays clear advantages over the other existing ones.

arXiv:1105.4815•May 24, 2011•1 citation

Selective and Efficient Quantum Process Tomography with Single Photons

Christian Tomás Schmiegelow, M. A. Larotonda, Juan Pablo Paz

We present the results of the first photonic implementation of a new method for quantum process tomography. The method {originally presented by A. Bendersky et al. [Phys. Rev. Lett. 100, 190403 (2008)10.1103/PhysRevLett.100.190403]} enables the estimation of any element of the chi-matrix that characterizes a quantum process using resources that scale polynomially with the number of qubits. It is based on the idea of mapping the estimation of any chi-matrix element onto the average fidelity of a quantum channel and estimating the latter by sampling randomly over a special set of states called a 2-design. With a heralded single photon source we fully implement such algorithm and perform process tomography on a number of channels affecting the polarization qubit. The method is compared with other existing ones, and its advantages are discussed.

Physical Review Letters•Mar 24, 2010•28 citations

Selective and efficient quantum process tomography with single photons

Christian Tomás Schmiegelow, M. A. Larotonda, Juan Pablo Paz

We present the results of the first photonic implementation of a new method for quantum process tomography. The method (originally presented by A. Bendersky et al, Phys. Rev. Lett 100, 190403 (2008)) enables the estimation of any element of the chi-matrix that characterizes a quantum process using resources that scale polynomially with the number of qubits. It is based on the idea of mapping the estimation of any chi-matrix element onto the average fidelity of a quantum channel and estimating the latter by sampling randomly over a special set of states called a 2-design. With a heralded single photon source we fully implement such algorithm and perform process tomography on a number of channels affecting the polarization qubit. The method is compared with other existing ones and its advantages are discussed.

arXiv:1002.4436•Feb 23, 2010•0 citations

Selective and efficient quantum process tomography

Ariel Bendersky, Fernando Pastawski, Juan Pablo Paz

In this paper we describe in detail and generalize a method for quantum process tomography that was presented by Bendersky et al. [Phys. Rev. Lett. 100, 190403 (2008)]. The method enables the efficient estimation of any element of the $\ensuremath{\chi}$ matrix of a quantum process. Such elements are estimated as averages over experimental outcomes with a precision that is fixed by the number of repetitions of the experiment. Resources required implementing it scale polynomially with the number of qubits of the system. The estimation of all diagonal elements of the $\ensuremath{\chi}$ matrix can be efficiently done without any ancillary qubits. In turn, the estimation of all the off-diagonal elements requires an extra clean qubit. The key ideas of the method, which is based on efficient estimation by random sampling over a set of states forming a 2-design, are described in detail. Efficient methods for preparing and detecting such states are explicitly shown.

arXiv:0906.3002•Physical Review A•Sep 24, 2009•46 citations

Experimental characterization of quantum processes: A selective and efficient method in arbitrary finite dimensions

Quimey Pears Stefano, Ignacio Perito, J. J. M. Varga +2 more

The temporal evolution of a quantum system can be characterized by quantum process tomography, a complex task that consumes a number of physical resources scaling exponentially with the number of subsystems. An alternative approach to the full reconstruction of a quantum channel is the selective and efficient quantum process tomography, a method that allows estimating, individually and up to the required accuracy, each element of the matrix that describes the process, using only a polynomial amount of resources. The implementation of this protocol is closely related to the possibility of building a complete set of mutually unbiased bases (MUBs), whose existence is known only when the dimension of the Hilbert space is the power of a prime number. However, an extension of the method that uses tensor products of maximal sets of MUBs has been recently introduced. Here we explicitly describe how to implement the algorithm for a selective and efficient estimation of a quantum process in a nonprime power dimension and conduct, an experimental verification of the method in a Hilbert space of dimension $d=6$. This is the smallest space for which a complete set of MUBs is not known to exist, but it can be decomposed as a tensor product of two Hilbert spaces of dimensions ${D}_{1}=2$ and ${D}_{2}=3$, in which a complete set of MUBs is already known. The six-dimensional states were codified in the discretized transverse linear momentum of photons. The state preparation and detection stages are dynamically programed with the use of only-phase spatial light modulators, in a versatile experimental setup that allows one to implement the algorithm in any finite dimension.

arXiv:2011.08228•Physical Review A•May 28, 2021•2 citations

Compressed Quantum Process Tomography

Alireza Shabani, Robert L. Kosut, HERSCHEL A. RABITZ

The characterization of a decoherence process is among the central challenges in quantum physics. A major difficulty with current quantum process tomography methods is the enormous number of experiments needed to accomplish a tomography task. Here we present a highly efficient method for tomography of a quantum process that has a small number of significant elements. Our method is based on the compressed sensing techniques being used in information theory. In this new method, for a system with Hilbert space dimension n and a process matrix of dimension n × n with sparsity s, the required number of experimental configurations is O(s log n). This heralds a logarithmic advantage in contrast to other methods of quantum process tomography. More specifically, for q-qubits with n = 2, the scaling of resources is O(sq) — linear in the product of sparsity and number of qubits.

APS March Meeting Abstracts•Oct 28, 2009•1 citation
Several methods, known as quantum process tomography, are available to characterize the evolution of quantum systems, a task of crucial importance. However, their complexity dramatically increases with the size of the system. Here we present a new method for quantum process tomography. We describe a new algorithm that can be used to selectively estimate any parameter characterizing a quantum process. Unlike any of its predecessors this new quantum tomographer combines two virtues: it requires investing a number of physical resources scaling polynomially with the number of qubits and at the same time it does not require any ancillary resources. We present the results of the first implementation of this quantum device, characterizing quantum processes affecting two qubits encoded in heralded single photons. Even for this small system our method displays clear advantages over the other existing ones.
Several methods, known as Quantum Process Tomography, are available to characterize the evolution of quantum systems, a task of crucial importance. However, their complexity dramatically increases with the size of the system. Here we present the theory describing a new type of method for quantum process tomography. We describe an algorithm that can be used to selectively estimate any parameter characterizing a quantum process. Unlike any of its predecessors this new quantum tomographer combines two main virtues: it requires investing a number of physical resources scaling polynomially with the number of qubits and at the same time it does not require any ancillary resources. We present the results of the first photonic implementation of this quantum device, characterizing quantum processes affecting two qubits encoded in heralded single photons. Even for this small system our method displays clear advantages over the other existing ones.
We present the results of the first photonic implementation of a new method for quantum process tomography. The method {originally presented by A. Bendersky et al. [Phys. Rev. Lett. 100, 190403 (2008)10.1103/PhysRevLett.100.190403]} enables the estimation of any element of the chi-matrix that characterizes a quantum process using resources that scale polynomially with the number of qubits. It is based on the idea of mapping the estimation of any chi-matrix element onto the average fidelity of a quantum channel and estimating the latter by sampling randomly over a special set of states called a 2-design. With a heralded single photon source we fully implement such algorithm and perform process tomography on a number of channels affecting the polarization qubit. The method is compared with other existing ones, and its advantages are discussed.
We present the results of the first photonic implementation of a new method for quantum process tomography. The method (originally presented by A. Bendersky et al, Phys. Rev. Lett 100, 190403 (2008)) enables the estimation of any element of the chi-matrix that characterizes a quantum process using resources that scale polynomially with the number of qubits. It is based on the idea of mapping the estimation of any chi-matrix element onto the average fidelity of a quantum channel and estimating the latter by sampling randomly over a special set of states called a 2-design. With a heralded single photon source we fully implement such algorithm and perform process tomography on a number of channels affecting the polarization qubit. The method is compared with other existing ones and its advantages are discussed.
In this paper we describe in detail and generalize a method for quantum process tomography that was presented by Bendersky et al. [Phys. Rev. Lett. 100, 190403 (2008)]. The method enables the efficient estimation of any element of the $\ensuremath{\chi}$ matrix of a quantum process. Such elements are estimated as averages over experimental outcomes with a precision that is fixed by the number of repetitions of the experiment. Resources required implementing it scale polynomially with the number of qubits of the system. The estimation of all diagonal elements of the $\ensuremath{\chi}$ matrix can be efficiently done without any ancillary qubits. In turn, the estimation of all the off-diagonal elements requires an extra clean qubit. The key ideas of the method, which is based on efficient estimation by random sampling over a set of states forming a 2-design, are described in detail. Efficient methods for preparing and detecting such states are explicitly shown.
The temporal evolution of a quantum system can be characterized by quantum process tomography, a complex task that consumes a number of physical resources scaling exponentially with the number of subsystems. An alternative approach to the full reconstruction of a quantum channel is the selective and efficient quantum process tomography, a method that allows estimating, individually and up to the required accuracy, each element of the matrix that describes the process, using only a polynomial amount of resources. The implementation of this protocol is closely related to the possibility of building a complete set of mutually unbiased bases (MUBs), whose existence is known only when the dimension of the Hilbert space is the power of a prime number. However, an extension of the method that uses tensor products of maximal sets of MUBs has been recently introduced. Here we explicitly describe how to implement the algorithm for a selective and efficient estimation of a quantum process in a nonprime power dimension and conduct, an experimental verification of the method in a Hilbert space of dimension d=6d=6d=6. This is the smallest space for which a complete set of MUBs is not known to exist, but it can be decomposed as a tensor product of two Hilbert spaces of dimensions D1=2{D}_{1}=2D1​=2 and D2=3{D}_{2}=3D2​=3, in which a complete set of MUBs is already known. The six-dimensional states were codified in the discretized transverse linear momentum of photons. The state preparation and detection stages are dynamically programed with the use of only-phase spatial light modulators, in a versatile experimental setup that allows one to implement the algorithm in any finite dimension.
The characterization of a decoherence process is among the central challenges in quantum physics. A major difficulty with current quantum process tomography methods is the enormous number of experiments needed to accomplish a tomography task. Here we present a highly efficient method for tomography of a quantum process that has a small number of significant elements. Our method is based on the compressed sensing techniques being used in information theory. In this new method, for a system with Hilbert space dimension n and a process matrix of dimension n × n with sparsity s, the required number of experimental configurations is O(s log n). This heralds a logarithmic advantage in contrast to other methods of quantum process tomography. More specifically, for q-qubits with n = 2, the scaling of resources is O(sq) — linear in the product of sparsity and number of qubits.